Sun Angle Calculator — Solar Elevation & Azimuth
Find the exact angle of the sun above the horizon (elevation) and its compass bearing (azimuth) for any location, date and time. The daily elevation curve shows how the sun arcs through the sky.
°
°
h
h
Sun is above the horizon
- 1
Day of year N
187Day number 1 = 1 Jan. - 2
Solar declination δ = −23.45° × cos(2π/365 × (N+10))
−23.45° × cos(2π/365 × (187 + 10)) = 22.72° - 3
Equation of Time correction tc (min)
4 × (-74 − -4 × 15) + EoT = -60.36 minCorrects clock time to true solar time using longitude offset and orbital equation. - 4
Local solar time LST = local hour + tc ÷ 60
12 h + -60.36 ÷ 60 = 10.994 h - 5
Hour angle H = 15° × (LST − 12)
15° × (10.994 − 12) = -15.09° - 6
Solar elevation α = arcsin(sin φ sin δ + cos φ cos δ cos H)
67.97°
How does this calculator work?
Solar elevation = arcsin(sin(lat)sin(dec) + cos(lat)cos(dec)cos(H)), where declination dec = −23.45°×cos(2π/365×(N+10)) and hour angle H = 15°×(solar_time − 12). Azimuth = 180° + atan2(sin H, cos H·sin lat − tan dec·cos lat). Accurate to ≈0.2° for 1950–2050; no atmospheric refraction correction.
Formula
How this is calculated
The sun's apparent position is described by two angles: elevation (how far above the horizon) and azimuth (compass bearing clockwise from North). This calculator uses the simplified NOAA solar position algorithm, accurate to within approximately 0.2° for dates between 1950 and 2050.
Solar declination δ (the sun's north–south position relative to the equator) is computed from day of year N: δ = −23.45°×cos(2π/365×(N+10)). The Equation of Time (EoT) corrects clock time to true solar time by accounting for Earth's elliptical orbit and axial tilt — it varies between −16 and +14 minutes across the year. After applying the longitude offset and EoT the hour angle H = 15°×(local_solar_time − 12) measures how far the sun has rotated from solar noon. These three quantities go into the elevation formula.
The azimuth Az = 180° + atan2(sin H, cos H·sin φ − tan δ·cos φ) gives the compass bearing with North = 0°, East = 90°, South = 180°. The formula is not corrected for atmospheric refraction, which lifts the apparent sun by 0.5°–1° near the horizon, so sunrise and sunset times from this model may be off by one to two minutes relative to published almanac values.
Frequently asked questions
Solar elevation (altitude) is the angle of the sun above the horizon: 0° at sunrise/sunset, maximum at solar noon. It determines the intensity of sunlight — the higher the elevation, the more direct the radiation per unit area. Below 0° the sun is below the horizon.
Azimuth is the sun's compass bearing measured clockwise from North (0° = N, 90° = E, 180° = S, 270° = W). In the Northern Hemisphere the sun transits near 180° (south) at noon; in the Southern Hemisphere it transits near 0° (north).
Solar noon depends on your actual longitude within the time zone and the Equation of Time. Time zones span 15° of longitude each, so a location at the far edge can be up to ±30 minutes off clock noon, plus the EoT shifts it another ±16 minutes.
Also known as
TG we-Calculate Editorial Team. (2026). Sun Angle Calculator — Solar Elevation & Azimuth [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sun-angle-calculator
TG we-Calculate Editorial Team. "Sun Angle Calculator — Solar Elevation & Azimuth." TG we-Calculate. 2026. https://we-calculate.com/calculator/sun-angle-calculator.
TG we-Calculate Editorial Team, "Sun Angle Calculator — Solar Elevation & Azimuth," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sun-angle-calculator
@misc{wecalculate_sun_angle_calculator, title = {Sun Angle Calculator — Solar Elevation & Azimuth}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sun-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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